Finding out if vectors are Parallel or Orthogonal in Parametric Form.

Question

I have two Parametric Form Vectors. Is it possible in that form to work out if the vectors are Parallel, Orthogonal or neither. Or do I have to have it in standard vector form $ (a_1, a_2, a_3)$ and then just use the dot product there.

$R_1 = (x+5)/(-5) = (y - 8)/(2) = (z+54)/-45 $ $R_2 = (x+12)/(-105) = (y - 10)/(-48) = (z+6)/444 $

Can I use dot product when the vectors are in Parametric form, and how does it work??

Answer 1

These are lines with direction vectors $(-5, 2, -45)$ and $(-105, -48, 444)$. You can use dot product of the direction vectors to see if the lines are perpendicular or orthogonal.